Comparison of Frequency Offset Estimation Methods for OFDM Burst Transmission in the Selective Fading Channels

Transcription

1 Compariso of Frequecy Offset Estimatio Methods for OFDM Burst Trasmissio i the Selective Fadig Chaels Zbigiew Długaszewski Istitute of Electroics ad Telecommuicatios Pozań Uiversity of Techology Pozań, Polad zdlugasz@etputpozapl ABSTRACT I this paper the performace ad complexity of several frequecy offset estimatio schemes for the OFDM (Orthogoal Frequecy Divisio Multiplexig) burst trasmissio i the selective fadig chaels have bee compared This topic becomes especially importat sice the frequecy offset icreases with user speed o oe had, ad the trasmissio systems eg wireless local area etworks (WLAN) migrate to higher ad higher frequecy bads where IF ad RF oscillators are less stable tha at lower frequecies o the other had I the OFDM systems the frequecy offset f ca be ormalized to the subcarrier spacig f Most of the aalyzed algorithms estimate frequecy offset which is a iteger multiple of the subcarrier spacig I INTRODUCTION WLANs become a hot topic of iterest because of icreasig demad for mobile high data rate trasmissio systems The demad for the WLAN systems will grow i the future ad ew systems have to be developed Such a system, operatig i 17 GHz bad, is developed withi the WIND-FLEX project [1] Recetly the OFDM modulatio has become very popular method of digital trasmissio ad has bee proposed for trasmissio i the multipath radio chaels The OFDM modulatio is spectrally efficiet ad has high immuity to the IterSymbol Iterferece (ISI) due to the relatively low data rate at subcarriers ad the applicatio of a cyclic prefix However, it has also some serious drawbacks, such as sesitivity of the system performace to the frequecy offset ad to the ifluece of selective fadig The frequecy offset is uavoidable i burst trasmissio i the WLAN systems Its sources are the Doppler shift ad, first of all, the differeces betwee local oscillators at the trasmitter ad receiver Such a offset destroys the orthogoality betwee the OFDM symbol subcarriers ad itroduces ICI at the output of the OFDM demodulator Whe the frequecy offset is larger tha the subcarrier spacig f, a circular shift of the samples at the FFT output ca be additioally observed Thus, the total frequecy offset ca be ormalized to the subcarrier spacig ad divided ito two parts: the iteger ad the fractioal oes Several methods of the estimatio of the frequecy offset i the OFDM systems ca be foud i the literature [-10] Most of these methods are able to estimate the iteger part ad some others ca do it for the whole frequecy offset Geerally, the algorithms operatig i the frequecy domai are able to estimate iteger part of the frequecy offset oly ad require the fractioal part to be removed prior to the FFT The wireless modem, which is beig desiged withi the 5FW WIND-FLEX project, will trasmit 100 Mbps of user data ad the DSP processig must be realized i hardware (FPGA) Such a solutio imposes restrictios o the algorithm complexity because of the limited silico space ad the achievable processig speed I this paper some of the carrier sychroizatio methods have bee compared from the complexity ad the performace poit of view I Sectio II the OFDM system outlie ad sychroizatio preamble used i the burst trasmissio system have bee preseted Algorithms ad their complexity have bee preseted i Sectio III I Sectio IV simulatio results obtaied i the selective fadig chaels have bee show Coclusios have bee draw i Sectio V As already metioed, this work has bee doe withi the WIND-FLEX project ad its motivatio was to fid a suitable frequecy offset estimatio method for the WIND-FLEX modem II SYSTEM OUTLINE Burst trasmissio requires special symbols (preambles) for the sychroizatio purposes at the begiig of each frame All frequecy offset estimatio algorithms examied i this paper use oly oe OFDM symbol, which is the first preamble symbol at the begiig of the frame This symbol cosists of two idetical short symbols, which are used by the timig offset estimatio algorithm I such preamble symbol oly eve subcarriers are trasmitted (the subcarrier spacig is twice as large as i the other symbols) I real systems, some subcarriers at the edges of the sigal spectrum have to be switched off as well This is caused by the requiremets imposed by digital filterig ad is also aimed to decrease iterferece itroduced ito the eighborig chaels I order to obtai two idetical short preamble symbols, also the DC subcarrier has to be switched off Additioally, oe of the preseted methods requires some additioal subcarriers ear the DC to be switched off as well

2 Simulated OFDM system has bee show i Figure 1 I case whe the simulated algorithm works i the time domai (like i [9]), the frequecy offset estimatio algorithm is represeted by block No1 ad the OFDM sigal demodulatio is ot required However, other studied algorithms work i the frequecy domai (block No ) ad the demodulator realized by the FFT is eeded These algorithms require removal of the fractioal part of the frequecy offset prior to the sigal demodulatio ad i such case this fuctio is performed i block No 1 D block No OFDM modulator Y k b FFT filters frequecy offset block No1 Chael & freq offset y filters Figure 1 OFDM system scheme Most of the frequecy offset estimatio algorithms preseted i the literature are based o the Maximum Likelihood (ML) criterio May algorithms are carried out by the search for the maximum of the correlatio betwee received samples, pilot toes or some fuctios of the received pilot toes Usig oly oe preamble symbol, the estimate of the frequecy offset must be obtaied by maximizatio of the correlatio betwee the kow trasmitted symbol ad the received symbol III ALGORITHMS AND THEIR COMPLEXITY Two of the aalyzed algorithms geerate a sigal with the frequecy equal to the carrier frequecy offset This is doe at the receiver, which should strip the received sigal y of the cotets of the trasmitted data ad leave a umodulated pure toe at the frequecy equal to the frequecy offset However, this is truly possible for the AWGN chael oly It may happe that the desired toe is atteuated due to fadig ad caot be detected correctly Two slightly differet approaches to achieve the pure toe have bee preseted i [] ad [9] I [], the referece sigal R() is defied as R ( ) = b b (see Figure 1) Multiplyig such a referece sigal by the received sigal y k oe obtais the sigal F() I case of the AWGN chael ad the frequecy offset f, F() ca be writte as ( j π ft + θ ) F( ) = b y b exp s I [9], ormalizatio of the received sigal amplitude has bee carried out usig y k istead of b k The pure toe sigal is created as follows b y F( ) = exp s b y ( j π ft + θ ) The procedure proposed i [] requires oly the multiplicatio of the received samples y by the stored values R() The ormalizatio from [9] is much more complex It requires calculatio of the absolute value ad a real divisio Most of the calculatios preseted below are performed o complex variables ad oe complex multiplicatio requires four real multiplicatios ad two additios Implemetatio of a real divisio ad a square root are much more complex tha all other operatios As we have metioed, most of the algorithms aalyzed below are executed after the OFDM symbol demodulatio Sice the FFT must be implemeted at the receiver i ay case, the complexity of the FFT operatio has ot bee take ito accout I order to determie the existig frequecy offset all these algorithms require also implemetatio of search for the miimum or the maximum value Sice the acquisitio rage of these algorithms is much larger tha the frequecy offset existig i real systems R, ot all correlatio/metrics values must be calculated ad compared A FFT of the pure toe sigal This algorithm has bee preseted i [] ad a similar idea was preseted i [3] At the first step, the pure toe sigal F() is calculated The frequecy offset f is estimated i the frequecy domai usig the FFT I [] the iterpolatio techique has bee proposed to improve the accuracy of the calculated frequecy offset estimate The iterpolatio is eable to joitly estimate a fractioal ad a iteger part of the frequecy offset I our studies we have examied iterpolatio by the secod order polyomial (algorithm A1), ad the case whe o iterpolatio has bee applied (algorithm A) I the latter case the estimator returs the idex of the sigal magitude peak (hard output) The iterpolatio techique reported i [] has bee also examied The algorithm performace has bee also tested i combiatio with the secod method of a pure toe acquisitio preseted before The acquisitio rage of this algorithm is equal to f < BW, where BW is the sigal badwidth The estimator is able to calculate correct estimates as log as the peak value stads out agaist the oise level ad there is o fade i the basebad equivalet chael at the frequecy equal to the carrier frequecy offset The algorithm requires calculatio of N pure toe samples before the FFT Additioally, oly R calculatios of the sigal power are required i the simplest case whe the hard decisio output is obtaied Applicatio of iterpolatio slightly icreases computatioal requiremets B Correlatio of the sigature sequeces This algorithm (deoted as B) has bee preseted i [4] I order to evaluate the iteger part of the frequecy offset, its authors propose to correlate sigature sequeces geerated from the kow ad received preamble symbols The sigature sequeces are defied for the trasmitted subcarrier toes oly ad are described by the formulae: YlYl + DlDl+ u = l ad v = l Y Y D D l l + l l+

3 where Y l ad D l are the received sample at the FFT output ad trasmitted data for pilot toes, respectively Oe ca otice that such a defiitio of the sigature sequece elimiates the ifluece of the chael atteuatio ad phase shift (oe ca assume that the phase of the chael trasfer fuctio does ot differ much betwee two cosecutive pilot toes) The correlatio B(m) betwee the sigature sequeces is defied as u v + l l m ( u ) l B ( m) Precisio of the estimate is equal to the spacig betwee the trasmitted pilot toes ( f 1 = f) The acquisitio rage of this algorithm is equal to m < N 4, where N is the FFT size (umber of subcarriers) N real divisios, N/ multiplicatios ad computatio of the absolute value are required to calculate the sigature sequece u l Computatio of the correlatio fuctio B(m) requires N additios, N/ multiplicatios, N complex ad real calculatios of power ad oe real divisio for each m C Correlatio withi the Coherece Phase Badwidth This algorithm has bee proposed i [5] ad is a modificatio of the algorithms preseted i [6] ad [7] It estimates the iteger frequecy offset by correlatio betwee the kow pilot symbols ad the received oes Authors of this algorithm itroduce the coherece phase badwidth BW C cocept as the maximum itegratio rage with respect to the allowed symbol timig offset T allow : BWC BW T allow, where BW deotes the sigal badwidth The sigal badwidth is divided ito K blocks of the width equal to BW C ad correlatios are calculated separately for each block The estimate of the coarse frequecy offset i [6] (algorithm C1) is obtaied by maximizatio the correlatio betwee symbols: N 1 k = 0 Cor ( m ) = D Y k ( k + m) mod N The authors of [5] propose to maximize the followig fuctio (algorithm C): CorM ( m ) K = 1 BW i= 0 k = 0 C D Y k + i BWC ( k + i BWC + m) mod N The acquisitio rage of this algorithm is equal to m < N Each correlatio requires N multiplicatios ad additios The modificatio proposed i [5] requires K additios ad some calculatios of absolute values D Search for ull i the preamble symbol spectrum This algorithm has bee proposed i [8] ad relies o the calculatio of metrics M(m) based o the received subcarrier power The metric (algorithm D1) is defied as follows: M 1+ ex ( m) =, ex Y + i i= 1 ex where the parameter ex is a small positive umber ad defies the spectrum ull width Miimum of metric idicates the estimated frequecy offset (or a positio of the ull i the middle of the sigal spectrum) Oe ca otice that this algorithm is immue to a costat phase shift (eg caused by timig errors) sice it uses received subcarriers power oly To improve the algorithm performace we have to icrease the summig rage i order to average larger amout of oise Sice we kow that oly eve subcarriers are trasmitted, we ca add oise power received at odd subcarriers ad subtract power received at eve subcarriers Such a procedure i fact relies o correlatio betwee the received symbol power spectrum ad some mask with +1 for uused subcarriers ad 1 for trasmitted subcarriers The metric (algorithm D) ca be writte as follows: N / 1 i= N / ; i uused N / 1 + i j= N / ; j set M ( = x x F, ex ) + j The acquisitio rage of this algorithm is greater tha N 4 Calculatio of the metric i the latter case requires N calculatios of powers ad additios The total umber of additios i both preseted cases ca be sigificatly reduced E Correlatio i the time domai This method was preseted i [9] This algorithm works i the time domai (it does ot require calculatio of the FFT) ad is able to estimate the overall frequecy offset existig i the system (joitly a fractioal ad a iteger part) The algorithm has bee derived from a geeral problem of fidig the ML estimator of the frequecy offset f from the pure toe F( t) = exp( jπft) The frequecy offset estimator is described by the formula: M fˆ 1 = arg C( m), πt ( M + 1) s m= 1 where T s is the samplig period ad C(m) deotes the autocorrelatio defied by Q 1 C( m) = F F, 1, 1 1 m M M Q k Q m = k + 1 Estimator has bee examied i combiatio with both methods of pure toe geeratio The parameters M ad Q (M < Q N) determie the algorithm s sesitivity ad its operatig rage Geerally Q should be as large as possible (equal N) The operatig (or i our case acquisitio) rage of this algorithm is equal to f < 1 ( M + 1) T s Calculatio of the estimate requires oe calculatio of the arc taget fuctio, M+1 real ad M(Q-M- 1)/ complex multiplicatios ad M additios The algorithm also requires the calculatio of the pure toe sigal F Compariso - the algorithms complexity criterio The algorithm complexity plays crucial role i the system desig process sice the realizatio of may accu-

4 rate divisios ad/or square root operatios operatig at very high speed is impossible usig existig FPGA chips Table below summarizes the umber of operatios required by each algorithm All operatios are real Algorithms B, C ad E require calculatio of the square root (as well as algorithms A1-A3 for the alterative pure toe calculatio) ad this makes them difficult to implemet Algorithms A are more computatioally demadig i compariso to the algorithms D due to the calculatio of the pure toe sigal Geerally, algorithms D require the lowest umber of multiplicatios ad additios Table 1 Compariso of algorithm complexity (umber of real operatios) Alg + / others A1 4N+R+4 R+N+6 1 A 4N+R R+N - B N (R+1) 4RN+3/N N+R N/ sqrt() +R+N C1 4RN 4RN - - C 4RN 4RN+3RK - RK sqrt() D1 (R+4ex+) R+4ex R(4ex+3) D N N+R(ex+1) - - E M(N-M) -M-1+6N M(N-M)+3N N N sqrt() 1 ata() E M(N-M) -M-1+4N M(N-M)+N 1 ata() i case of the secod pure toe acquisitio techique additioally N multiplicatios, N divisios, additios ad square root calculatios are required the first pure toe acquisitio techique The performace of the algorithms ca be compared by meas of the simulatio Such a compariso has bee preseted i the ext sectio IV SIMULATION RESULTS All results preseted below have bee obtaied for the WIND-FLEX sceario N, the umber of the FFT size (ad umber of subcarriers i the OFDM symbol) was equal 18 All algorithms have bee simulated for differet realizatios of the NLOS (No Lieof-Sight) chael model created for the WIND-FLEX project [11] Oe ca compare the results obtaied for differet values of ucompesated fractioal part of the frequecy offset ad differet sigal-to-oise (SNR) values This offset causes ICI ad atteuates subcarrier amplitudes o the FFT output I systems with may subcarriers ICI ca be treated as a AWGN ad that is why the results obtaied at the presece of low fractioal part of the frequecy offset do ot differ much amog themselves For the algorithm C the parameter K was equal to 4 ad 16 I case of the algorithms D the parameter ex was equal to For the algorithm E parameter Q was equal to N ad the parameter M was equal to 9, 15 ad 4 These values correspod to the acquisitio rage equal to 5 MHz, 315 MHz ad MHz (the samplig time T s was equal to 0 s) All tables preseted below show the percetage of correct estimates of the iteger part of the frequecy offset for differet SNR values ad differet ucompesated fractioal parts of the frequecy offset f A fractioal part of the frequecy offset is expressed as a percetage of the subcarrier spacig The performace of algorithms A depeds o the applied method of the pure toe acquisitio Some results have bee collected i Table show below Sice the pure toe sigal is calculated prior to the FFT, calculated frequecy offset is rouded to the iteger multiple of the subcarrier spacig i case of the algorithm A The algorithm A1 calculates the overall frequecy offset but the iteger part of the frequecy offset is almost idetical for the algorithm A1 ad A The results with the origial iterpolatio techique (from []) have ot bee show because of their poor performace Decreasig SNR i the examied rage oly slightly lowers the reliability of the calculated estimate Table Performace of algorithms A for differet pure toe acquisitio techique SNR pure toe [] pure toe [9] 16dB 930% 9889% 11dB 905% 9889% 6dB 9140% 9885% The simulatio results obtaied for the algorithm B have bee show below The algorithm was able to calculate correct estimate of the frequecy offset i all examied cases The results obtaied for the algorithm C (for both examied value of the parameter K) have bee preseted below I all cases 100% of correct estimates have bee obtaied, similarly as for the algorithm B These algorithms require the greatest umber of computatios icludig calculatio of the square root fuctio Table 3 Performace of algorithm B SNR f = 0% f = 5% f = 10% f = 15% f = 0% 16dB 1000% 1000% 1000% 1000% 1000% 11dB 1000% 1000% 1000% 1000% 1000% 6dB 1000% 1000% 1000% 1000% 1000% Table 4 Performace of algorithm C1 SNR f = 0% f = 5% f = 10% f = 15% f = 0% 16dB 9987% 9987% 9986% 9986% 9985% 11dB 9987% 9986% 9986% 9985% 9985% 6dB 9985% 9985% 9985% 9984% 9983% Table 5 Performace of algorithm C (for both K) SNR f = 0% f = 5% f = 10% f = 15% f = 0% 16dB 10000% 10000% 10000% 10000% 10000% 11dB 10000% 10000% 10000% 10000% 10000% 6dB 10000% 10000% 10000% 10000% 10000% The algorithm C1 offers worse performace i the compariso with algorithms B ad C, but it requires lower complexity The algorithm performace depeds very slightly o the SNR ad ucompesated fractioal part of the frequecy offset ad is higher tha that obtaied for algorithms A, D ad E The results obtaied for the algorithms D1 ad D have bee show i Table 6 ad Table 7 The frequecy offset estimates calculated by the algorithm D1 are sesitive to the oise (AWGN ad caused by the ICI) The

5 algorithm D is much more robust tha the algorithm D1, however performs worse tha the algorithm C1 Table 6 Performace of algorithm D1 SNR f = 0% f = 5% f = 10% f = 15% f = 0% 16dB 9933% 9917% 9850% 974% 954% 11dB 9840% 9815% 9741% 9605% 9387% 6dB 9497% 946% 9375% 919% 8950% Table 7 Performace of algorithm D SNR f = 0% f = 5% f = 10% f = 15% f = 0% 16dB 9954% 9950% 9934% 9903% 9861% 11dB 9893% 9887% 9864% 988% 9773% 6dB 9665% 9650% 960% 9560% 9480% The performace of the algorithm E depeds o the value of the parameter M For smaller M (the results have ot bee preseted here) the obtaied estimates of the frequecy offset are less accurate tha these preseted below This is caused by the fact that the estimator variace depeds o the parameter M The algorithm E calculates the overall frequecy offset ad the estimate was rouded to the earest iteger multiple of the subcarrier spacig for the compariso purposes All preseted results have bee obtaied with the pure toe acquisitio techique proposed i [9] Table 8 Performace of algorithm E (M=4) SNR f = 0% 16dB 959% 11dB 957% 6dB 949% Simulatio results obtaied with algorithms A ad E show that better results have bee obtaied with the secod techique of the pure toe acquisitio (proposed i [9]) However, this techique requires calculatios of the square root ad that is why it should be avoided V CONCLUSIONS This paper compares several frequecy offset estimatio methods for OFDM systems The decisio, which of them should be implemeted, depeds o the performace aalysis ad the algorithm complexity Preseted simulatio results show that some of the ivestigated algorithms (algorithm B ad C) were able to provide correct estimates of the frequecy offset for examied SNR values, i presece of small amout of ICI i the frequecy selective chaels i 100% cases However, the computatioal complexity of these algorithms is very high The algorithms A ad E are sesitive to selective fadig ad require calculatio of the pure toe sigal The algorithm E has poor accuracy of the estimated offset, eve with limited acquisitio rage The algorithm D is oe of the simplest from the computatioal poit of view ad offers relatively high accuracy of the frequecy offset estimate (995% correct estimates for 16 db SNR ad almost 99% for 11 db SNR) Two differet frequecy offset estimatio algorithms are beig implemeted i the WIND-FLEX modem Oe of them, workig i the time domai, is able to estimate the fractioal part of the frequecy offset with precisio to 5% of the subcarrier spacig (i the acquisitio mode) I this rage of the fractioal part of the frequecy offset the differece i performace betwee algorithms C1 ad D is lower tha 1% for medium ad high SNR This is why the algorithm D has bee chose for the implemetatio i the WIND-FLEX demostrator ACKNOWLEDGEMENTS The author would like to thak Professor K Wesołowski from Pozań Uiversity of Techology for his helpful commets The author was awarded by the Foudatio for Polish Sciece with the Aual Stiped for Youg Scietists i year 00 This work has bee doe withi the WIND-FLEX project (Wireless Idoor Flexible High Bitrate Modem Architectures IST ) REFERENCES [1] I Saarie, et al, Mai approaches for the desig of wireless idoor flexible high bit rate WIND-FLEX modem architecture, IST Mobile Commuicatios Summit, Galway, October 000 [] H Kobayashi, A Novel Symbol Frame ad Carrier Frequecy Sychroizatio for Burst Mode OFDM Sigal, Proceedigs of VTC 000 Fall [3] K Taura, M Tsujishita, M Takeda, H Kato, A digital audio broadcastig (DAB) receiver, IEEE Tras Cosumer Electro, Vol 4, August 1996 [4] Y S Lim, JH Lee, A Efficiet Carrier Frequecy Offset Estimatio Scheme for a OFDM System, Proceedigs of VTC 000 Fall [5] K Bag, N Cho, J Cho, H Ju, K Kim, H Park, D Hog, A Coarse Frequecy Offset Estimatio i a OFDM System Usig the Cocept of the Coherece Phase Badwidth, IEEE Tras COM, Vol 49, No 8, August 001, pp [6] H Nogami, T Nagashima, A Frequecy ad Timig Period Acquisitio Techique for OFDM Systems, Proceedigs of PIMRC 1995, pp [7] T M Schmidl, D C Cox, Robust Frequecy ad Timig Sychroizatio for OFDM, IEEE Tras COM, Vol 45, No 1, December 1997, pp [8] Z Długaszewski, K Wesołowski, Simple Coarse Frequecy Offset Estimatio Schemes for OFDM Burst Trasmissio, submitted to PIMRC 00 [9] M Luise, R Reggiaii, Carrier Frequecy Acquisitio ad Trackig for OFDM Systems, IEEE Tras COM, Vol44, No 11, November 1996, pp [10] P H Moose, A techique for orthogoal frequecy divisio multiplexig frequecy offset correctio, IEEE Tras COM, Vol 4, October 1994, pp [11] M Lobeira, A Armada, R Torres, J L Garcia, Parameter estimatio ad idoor chael modellig at 17 GHz for OFDM-based broadbad WLAN, IST Mobile Commuicatios Summit, Galway, October 000